Distributed Bragg Reflector¶

A Distributed Bragg Reflector or DBR is an optical structure that consists of multiple alternating layers of materials with different refractive indices. The primary function of a DBR is to reflect specific wavelengths of light through constructive and destructive interference, making it an essential component in various optical devices such as vertical cavity surface emitting lasers.
The LayeredMediaSolver in JCMsuite can be used to simulate the reflectivity of this simple multilayer geometry:
project.jcmp [ASCII]
PostProcess {
  LayeredMediaSolver {
    OutputFileName = "result.jcm"
     LayerThickness = [9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07; 9.61538461538461e-08; 1.66666666666667e-07;]
     RelPermittivityInLayers=[1; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 6.76; 2.25; 2.25;]
     Lambda0 = [6e-07 6.005e-07 6.01e-07 6.015e-07 6.02e-07 6.025e-07 6.03e-07 6.035e-07 6.04e-07 6.045e-07 6.05e-07 6.055e-07 6.06e-07 6.065e-07 6.07e-07 6.075e-07 6.08e-07 6.085e-07 6.09e-07 6.095e-07 6.1e-07 6.105e-07 6.11e-07 6.115e-07 6.12e-07 6.125e-07 6.13e-07 6.135e-07 6.14e-07 6.145e-07 6.15e-07 6.155e-07 6.16e-07 6.165e-07 6.17e-07 6.175e-07 6.18e-07 6.185e-07 6.19e-07 6.195e-07 6.2e-07 6.205e-07 6.21e-07 6.215e-07 6.22e-07 6.225e-07 6.23e-07 6.235e-07 6.24e-07 6.245e-07 6.25e-07 6.255e-07 6.26e-07 6.265e-07 6.27e-07 6.275e-07 6.28e-07 6.285e-07 6.29e-07 6.295e-07 6.3e-07 6.305e-07 6.31e-07 6.315e-07 6.32e-07 6.325e-07 6.33e-07 6.335e-07 6.34e-07 6.345e-07 6.35e-07 6.355e-07 6.36e-07 6.365e-07 6.37e-07 6.375e-07 6.38e-07 6.385e-07 6.39e-07 6.395e-07 6.4e-07 6.405e-07 6.41e-07 6.415e-07 6.42e-07 6.425e-07 6.43e-07 6.435e-07 6.44e-07 6.445e-07 6.45e-07 6.455e-07 6.46e-07 6.465e-07 6.47e-07 6.475e-07 6.48e-07 6.485e-07 6.49e-07 6.495e-07 6.5e-07 6.505e-07 6.51e-07 6.515e-07 6.52e-07 6.525e-07 6.53e-07 6.535e-07 6.54e-07 6.545e-07 6.55e-07 6.555e-07 6.56e-07 6.565e-07 6.57e-07 6.575e-07 6.58e-07 6.585e-07 6.59e-07 6.595e-07 6.6e-07 6.605e-07 6.61e-07 6.615e-07 6.62e-07 6.625e-07 6.63e-07 6.635e-07 6.64e-07 6.645e-07 6.65e-07 6.655e-07 6.66e-07 6.665e-07 6.67e-07 6.675e-07 6.68e-07 6.685e-07 6.69e-07 6.695e-07 6.7e-07 6.705e-07 6.71e-07 6.715e-07 6.72e-07 6.725e-07 6.73e-07 6.735e-07 6.74e-07 6.745e-07 6.75e-07 6.755e-07 6.76e-07 6.765e-07 6.77e-07 6.775e-07 6.78e-07 6.785e-07 6.79e-07 6.795e-07 6.8e-07 6.805e-07 6.81e-07 6.815e-07 6.82e-07 6.825e-07 6.83e-07 6.835e-07 6.84e-07 6.845e-07 6.85e-07 6.855e-07 6.86e-07 6.865e-07 6.87e-07 6.875e-07 6.88e-07 6.885e-07 6.89e-07 6.895e-07 6.9e-07 6.905e-07 6.91e-07 6.915e-07 6.92e-07 6.925e-07 6.93e-07 6.935e-07 6.94e-07 6.945e-07 6.95e-07 6.955e-07 6.96e-07 6.965e-07 6.97e-07 6.975e-07 6.98e-07 6.985e-07 6.99e-07 6.995e-07 7e-07 7.005e-07 7.01e-07 7.015e-07 7.02e-07 7.025e-07 7.03e-07 7.035e-07 7.04e-07 7.045e-07 7.05e-07 7.055e-07 7.06e-07 7.065e-07 7.07e-07 7.075e-07 7.08e-07 7.085e-07 7.09e-07 7.095e-07 7.1e-07 7.105e-07 7.11e-07 7.115e-07 7.12e-07 7.125e-07 7.13e-07 7.135e-07 7.14e-07 7.145e-07 7.15e-07 7.155e-07 7.16e-07 7.165e-07 7.17e-07 7.175e-07 7.18e-07 7.185e-07 7.19e-07 7.195e-07 7.2e-07 7.205e-07 7.21e-07 7.215e-07 7.22e-07 7.225e-07 7.23e-07 7.235e-07 7.24e-07 7.245e-07 7.25e-07 7.255e-07 7.26e-07 7.265e-07 7.27e-07 7.275e-07 7.28e-07 7.285e-07 7.29e-07 7.295e-07 7.3e-07 7.305e-07 7.31e-07 7.315e-07 7.32e-07 7.325e-07 7.33e-07 7.335e-07 7.34e-07 7.345e-07 7.35e-07 7.355e-07 7.36e-07 7.365e-07 7.37e-07 7.375e-07 7.38e-07 7.385e-07 7.39e-07 7.395e-07 7.4e-07 7.405e-07 7.41e-07 7.415e-07 7.42e-07 7.425e-07 7.43e-07 7.435e-07 7.44e-07 7.445e-07 7.45e-07 7.455e-07 7.46e-07 7.465e-07 7.47e-07 7.475e-07 7.48e-07 7.485e-07 7.49e-07 7.495e-07 7.5e-07 7.505e-07 7.51e-07 7.515e-07 7.52e-07 7.525e-07 7.53e-07 7.535e-07 7.54e-07 7.545e-07 7.55e-07 7.555e-07 7.56e-07 7.565e-07 7.57e-07 7.575e-07 7.58e-07 7.585e-07 7.59e-07 7.595e-07 7.6e-07 7.605e-07 7.61e-07 7.615e-07 7.62e-07 7.625e-07 7.63e-07 7.635e-07 7.64e-07 7.645e-07 7.65e-07 7.655e-07 7.66e-07 7.665e-07 7.67e-07 7.675e-07 7.68e-07 7.685e-07 7.69e-07 7.695e-07 7.7e-07 7.705e-07 7.71e-07 7.715e-07 7.72e-07 7.725e-07 7.73e-07 7.735e-07 7.74e-07 7.745e-07 7.75e-07 7.755e-07 7.76e-07 7.765e-07 7.77e-07 7.775e-07 7.78e-07 7.785e-07 7.79e-07 7.795e-07 7.8e-07 7.805e-07 7.81e-07 7.815e-07 7.82e-07 7.825e-07 7.83e-07 7.835e-07 7.84e-07 7.845e-07 7.85e-07 7.855e-07 7.86e-07 7.865e-07 7.87e-07 7.875e-07 7.88e-07 7.885e-07 7.89e-07 7.895e-07 7.9e-07 7.905e-07 7.91e-07 7.915e-07 7.92e-07 7.925e-07 7.93e-07 7.935e-07 7.94e-07 7.945e-07 7.95e-07 7.955e-07 7.96e-07 7.965e-07 7.97e-07 7.975e-07 7.98e-07 7.985e-07 7.99e-07 7.995e-07 8e-07 8.005e-07 8.01e-07 8.015e-07 8.02e-07 8.025e-07 8.03e-07 8.035e-07 8.04e-07 8.045e-07 8.05e-07 8.055e-07 8.06e-07 8.065e-07 8.07e-07 8.075e-07 8.08e-07 8.085e-07 8.09e-07 8.095e-07 8.1e-07 8.105e-07 8.11e-07 8.115e-07 8.12e-07 8.125e-07 8.13e-07 8.135e-07 8.14e-07 8.145e-07 8.15e-07 8.155e-07 8.16e-07 8.165e-07 8.17e-07 8.175e-07 8.18e-07 8.185e-07 8.19e-07 8.195e-07 8.2e-07 8.205e-07 8.21e-07 8.215e-07 8.22e-07 8.225e-07 8.23e-07 8.235e-07 8.24e-07 8.245e-07 8.25e-07 8.255e-07 8.26e-07 8.265e-07 8.27e-07 8.275e-07 8.28e-07 8.285e-07 8.29e-07 8.295e-07 8.3e-07 8.305e-07 8.31e-07 8.315e-07 8.32e-07 8.325e-07 8.33e-07 8.335e-07 8.34e-07 8.345e-07 8.35e-07 8.355e-07 8.36e-07 8.365e-07 8.37e-07 8.375e-07 8.38e-07 8.385e-07 8.39e-07 8.395e-07 8.4e-07 8.405e-07 8.41e-07 8.415e-07 8.42e-07 8.425e-07 8.43e-07 8.435e-07 8.44e-07 8.445e-07 8.45e-07 8.455e-07 8.46e-07 8.465e-07 8.47e-07 8.475e-07 8.48e-07 8.485e-07 8.49e-07 8.495e-07 8.5e-07 8.505e-07 8.51e-07 8.515e-07 8.52e-07 8.525e-07 8.53e-07 8.535e-07 8.54e-07 8.545e-07 8.55e-07 8.555e-07 8.56e-07 8.565e-07 8.57e-07 8.575e-07 8.58e-07 8.585e-07 8.59e-07 8.595e-07 8.6e-07 8.605e-07 8.61e-07 8.615e-07 8.62e-07 8.625e-07 8.63e-07 8.635e-07 8.64e-07 8.645e-07 8.65e-07 8.655e-07 8.66e-07 8.665e-07 8.67e-07 8.675e-07 8.68e-07 8.685e-07 8.69e-07 8.695e-07 8.7e-07 8.705e-07 8.71e-07 8.715e-07 8.72e-07 8.725e-07 8.73e-07 8.735e-07 8.74e-07 8.745e-07 8.75e-07 8.755e-07 8.76e-07 8.765e-07 8.77e-07 8.775e-07 8.78e-07 8.785e-07 8.79e-07 8.795e-07 8.8e-07 8.805e-07 8.81e-07 8.815e-07 8.82e-07 8.825e-07 8.83e-07 8.835e-07 8.84e-07 8.845e-07 8.85e-07 8.855e-07 8.86e-07 8.865e-07 8.87e-07 8.875e-07 8.88e-07 8.885e-07 8.89e-07 8.895e-07 8.9e-07 8.905e-07 8.91e-07 8.915e-07 8.92e-07 8.925e-07 8.93e-07 8.935e-07 8.94e-07 8.945e-07 8.95e-07 8.955e-07 8.96e-07 8.965e-07 8.97e-07 8.975e-07 8.98e-07 8.985e-07 8.99e-07 8.995e-07 9e-07 9.005e-07 9.01e-07 9.015e-07 9.02e-07 9.025e-07 9.03e-07 9.035e-07 9.04e-07 9.045e-07 9.05e-07 9.055e-07 9.06e-07 9.065e-07 9.07e-07 9.075e-07 9.08e-07 9.085e-07 9.09e-07 9.095e-07 9.1e-07 9.105e-07 9.11e-07 9.115e-07 9.12e-07 9.125e-07 9.13e-07 9.135e-07 9.14e-07 9.145e-07 9.15e-07 9.155e-07 9.16e-07 9.165e-07 9.17e-07 9.175e-07 9.18e-07 9.185e-07 9.19e-07 9.195e-07 9.2e-07 9.205e-07 9.21e-07 9.215e-07 9.22e-07 9.225e-07 9.23e-07 9.235e-07 9.24e-07 9.245e-07 9.25e-07 9.255e-07 9.26e-07 9.265e-07 9.27e-07 9.275e-07 9.28e-07 9.285e-07 9.29e-07 9.295e-07 9.3e-07 9.305e-07 9.31e-07 9.315e-07 9.32e-07 9.325e-07 9.33e-07 9.335e-07 9.34e-07 9.345e-07 9.35e-07 9.355e-07 9.36e-07 9.365e-07 9.37e-07 9.375e-07 9.38e-07 9.385e-07 9.39e-07 9.395e-07 9.4e-07 9.405e-07 9.41e-07 9.415e-07 9.42e-07 9.425e-07 9.43e-07 9.435e-07 9.44e-07 9.445e-07 9.45e-07 9.455e-07 9.46e-07 9.465e-07 9.47e-07 9.475e-07 9.48e-07 9.485e-07 9.49e-07 9.495e-07 9.5e-07 9.505e-07 9.51e-07 9.515e-07 9.52e-07 9.525e-07 9.53e-07 9.535e-07 9.54e-07 9.545e-07 9.55e-07 9.555e-07 9.56e-07 9.565e-07 9.57e-07 9.575e-07 9.58e-07 9.585e-07 9.59e-07 9.595e-07 9.6e-07 9.605e-07 9.61e-07 9.615e-07 9.62e-07 9.625e-07 9.63e-07 9.635e-07 9.64e-07 9.645e-07 9.65e-07 9.655e-07 9.66e-07 9.665e-07 9.67e-07 9.675e-07 9.68e-07 9.685e-07 9.69e-07 9.695e-07 9.7e-07 9.705e-07 9.71e-07 9.715e-07 9.72e-07 9.725e-07 9.73e-07 9.735e-07 9.74e-07 9.745e-07 9.75e-07 9.755e-07 9.76e-07 9.765e-07 9.77e-07 9.775e-07 9.78e-07 9.785e-07 9.79e-07 9.795e-07 9.8e-07 9.805e-07 9.81e-07 9.815e-07 9.82e-07 9.825e-07 9.83e-07 9.835e-07 9.84e-07 9.845e-07 9.85e-07 9.855e-07 9.86e-07 9.865e-07 9.87e-07 9.875e-07 9.88e-07 9.885e-07 9.89e-07 9.895e-07 9.9e-07 9.905e-07 9.91e-07 9.915e-07 9.92e-07 9.925e-07 9.93e-07 9.935e-07 9.94e-07 9.945e-07 9.95e-07 9.955e-07 9.96e-07 9.965e-07 9.97e-07 9.975e-07 9.98e-07 9.985e-07 9.99e-07 9.995e-07 1e-06 1.0005e-06 1.001e-06 1.0015e-06 1.002e-06 1.0025e-06 1.003e-06 1.0035e-06 1.004e-06 1.0045e-06 1.005e-06 1.0055e-06 1.006e-06 1.0065e-06 1.007e-06 1.0075e-06 1.008e-06 1.0085e-06 1.009e-06 1.0095e-06 1.01e-06 1.0105e-06 1.011e-06 1.0115e-06 1.012e-06 1.0125e-06 1.013e-06 1.0135e-06 1.014e-06 1.0145e-06 1.015e-06 1.0155e-06 1.016e-06 1.0165e-06 1.017e-06 1.0175e-06 1.018e-06 1.0185e-06 1.019e-06 1.0195e-06 1.02e-06 1.0205e-06 1.021e-06 1.0215e-06 1.022e-06 1.0225e-06 1.023e-06 1.0235e-06 1.024e-06 1.0245e-06 1.025e-06 1.0255e-06 1.026e-06 1.0265e-06 1.027e-06 1.0275e-06 1.028e-06 1.0285e-06 1.029e-06 1.0295e-06 1.03e-06 1.0305e-06 1.031e-06 1.0315e-06 1.032e-06 1.0325e-06 1.033e-06 1.0335e-06 1.034e-06 1.0345e-06 1.035e-06 1.0355e-06 1.036e-06 1.0365e-06 1.037e-06 1.0375e-06 1.038e-06 1.0385e-06 1.039e-06 1.0395e-06 1.04e-06 1.0405e-06 1.041e-06 1.0415e-06 1.042e-06 1.0425e-06 1.043e-06 1.0435e-06 1.044e-06 1.0445e-06 1.045e-06 1.0455e-06 1.046e-06 1.0465e-06 1.047e-06 1.0475e-06 1.048e-06 1.0485e-06 1.049e-06 1.0495e-06 1.05e-06 1.0505e-06 1.051e-06 1.0515e-06 1.052e-06 1.0525e-06 1.053e-06 1.0535e-06 1.054e-06 1.0545e-06 1.055e-06 1.0555e-06 1.056e-06 1.0565e-06 1.057e-06 1.0575e-06 1.058e-06 1.0585e-06 1.059e-06 1.0595e-06 1.06e-06 1.0605e-06 1.061e-06 1.0615e-06 1.062e-06 1.0625e-06 1.063e-06 1.0635e-06 1.064e-06 1.0645e-06 1.065e-06 1.0655e-06 1.066e-06 1.0665e-06 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     IncidenceAngle = [20 22 24 26 28 30]
  }
}
The solver requires the definition of the thicknesses of the different layers in the vector LayerThickness and their material properties via the RelPermittivityInLayers. Here, the first and last entry are used to describe the relative permittivity on the incident and outgoing side. A definition of multiple vacuum wavelengths $\lambda_0$ in Lambda0 and $\theta$ angles in IncidenceAngle is allowed and yields the reflection spectrum in one simulation run.
The result is stored in the file result.jcm provided as the OutputFileName. It yields reflectivity and transmission values for both polarizations and for every combinations of $\lambda_0$ and $\theta$ stored in the output table.
These input parameters of the DBR and the required construction of the input for the project.jcmpt template are set in the run_project.m script. The reflectoin result is calculated and plotted as well.
Calculated reflectivity of DBR at normal incidence. Reflectivities of s and p polarized illumination are identical in this case.¶
Under non-normal incidence the polarization dependence of the reflectivity can be observed.
Calculated reflectivity of DBR at 20 degree incidence. Reflectivities of s and p polarized illumination deviate and lead to different widths of the stop band.¶